On partial orderings having precalibre-ℵ₁ and fragments of Martin's axiom
Joan Bagaria, Saharon Shelah (2016)
Fundamenta Mathematicae
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We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-ℵ₁, and show that Martin's axiom restricted to the class of partial orderings that have the property does not imply Martin's axiom for σ-linked partial orderings. This yields a new solution to an old question of the first author about the relative strength of Martin's axiom for σ-centered partial orderings together with the assertion that every Aronszajn tree is special. We also answer...